带数据图上的规则路径查询：一种刚性方法
Regular path queries on graphs with data: A rigid approach
摘要：
规则路径查询（RPQ）是一种经典的导航查询形式，用于图数据库指定标记路径上的约束。最近，Libkin和Vrgo $\rm \check{c}$扩展了RPQ，将路径上不同节点之间的数据值比较纳入其中，称为带数据的常规路径查询（RDPQ）。研究表明，RDPQ的评价问题在数据复杂度上是PSPACE完全和NLOGSPACE完全的。另一方面，RDPQ的包容问题一般是不可判定的。在本文中，我们提出了一种新的方法来扩展与数据值比较的常规路径查询，称为刚性规则路径查询与数据（RRDPQ）。这种方法的主要成分是一种称为非确定性刚性寄存器自动机（NRRA）的自动机模型，其中数据值比较是\emph{rigid}，在这个意义上，如果将当前位置$x$中的数据值与某个其他位置$y$中的数据值进行比较，则仅使用标签（而不是数据值），可以从$x$唯一地确定位置$y$。我们表明，NRRA是强大的，在这个意义上，非确定性，确定性和双向变体的NRRA，以及正则表达式的扩展，都是相同的表达。然后，我们认为RDPQ的表达能力是合理的，通过证明，对于每个图数据库，有一个本地化的图数据库的转换，使每个RDPQ在原始的图数据库可以变成一个等价的RRDPQ的转换。最后，我们研究了RRDPQ和合取RRDPQ（CRRDPQ）的计算性质。特别是，我们表明，CRRDPQ（和RRDPQ）的遏制可以决定在2EXPSPACE。
英文摘要：
Regular path queries (RPQ) is a classical navigational query formalism for graph databases to specify constraints on labeled paths. Recently, RPQs have been extended by Libkin and Vrgo$\rm \check{c}$ to incorporate data value comparisons among different nodes on paths, called regular path queries with data (RDPQ). It has been shown that the evaluation problem of RDPQs is PSPACE-complete and NLOGSPACE-complete in data complexity. On the other hand, the containment problem of RDPQs is in general undecidable. In this paper, we propose a novel approach to extend regular path queries with data value comparisons, called rigid regular path queries with data (RRDPQ). The main ingredient of this approach is an automata model called nondeterministic rigid register automata (NRRA), in which the data value comparisons are \emph{rigid}, in the sense that if the data value in the current position $x$ is compared to a data value in some other position $y$, then by only using the labels (but not data values), the position $y$ can be uniquely determined from $x$. We show that NRRAs are robust in the sense that nondeterministic, deterministic and two-way variant of NRRAs, as well as an extension of regular expressions, are all of the same expressivity. We then argue that the expressive power of RDPQs are reasonable by demonstrating that for every graph database, there is a localized transformation of the graph database so that every RDPQ in the original graph database can be turned into an equivalent RRDPQ over the transformed one. Finally, we investigate the computational properties of RRDPQs and conjunctive RRDPQs (CRRDPQ). In particular, we show that the containment of CRRDPQs (and RRDPQs) can be decided in 2EXPSPACE.
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